JERUSALEM — Plans for a truce devolved into threats of a wider war Tuesday as the first significant attempt to end more than a week of round-the-clock fire between Israel and Hamas ended before it even began.

The unraveling of an Egyptian cease-fire proposal offered little immediate hope for a diplomatic solution to a conflict that has left more than 190 Palestinians in Gaza dead and that Tuesday claimed its first Israeli fatality.

Israeli Prime Minister Benjamin Netanyahu gave the military authorization to use “full force” against militants in Gaza and vowed that Hamas and its allies would suffer for their decision not to halt their rocket fire into Israel.

“Hamas chose to continue fighting and will pay the price for that decision,” Netanyahu said in a televised address Tuesday evening. “When there is no cease-fire, our answer is fire.”

Netanyahu was under pressure from his right flank late Tuesday to authorize a risky ground invasion of Gaza aimed at ending Hamas’ reign as the de facto power in the coastal strip. Reflecting tensions within his government, Netanyahu fired his deputy defense minister for publicly accusing the Cabinet of not moving aggressively enough against Hamas.

The Islamist militant group also showed signs of internal strain, with its military wing vowing to escalate the conflict even as a top political leader said the group was considering Egypt’s cease-fire plan.

The proposal, offered late Monday, called for Israel and Hamas to stop firing Tuesday with no pre-conditions then start talks in Cairo within 48 hours.

Israel’s security Cabinet approved the deal Monday morning, and Israel stopped firing into Gaza at 9 a.m. local time. But Hamas officials balked at the proposal, saying they had never been consulted. The rocket fire from Gaza continued unabated, and Israel resumed military operations at 3 p.m.

The failure of the initiative reflected the absence of a diplomatic player with the clout and credibility to mediate the crisis. That role traditionally has been played by Egypt. But the country’s military-backed government is deeply hostile to Hamas, an Islamist militant off-shoot of Egypt’s Muslim Brotherhood, which Cairo authorities consider a terrorist organization.

“There’s a common denominator between Israel and Egypt, and that’s Hamas,” said former Israeli ambassador to Egypt Itzhak Levanon.

“Both really want to see Hamas weakened not only militarily but also politically. There’s a convergence of interests.”

That convergence led Egypt to spring the cease-fire proposal without prior warning late Monday night, said senior Hamas leader Sami Abu Zuhri, who described the move as a trap.

Hamas has said it will agree to a cease-fire only with preconditions and has set forth demands, including the reopening of Gaza’s crossing with Egypt and the release of hundreds of prisoners swept into Israeli jails last month.

By not agreeing to the truce, Hamas has taken some international pressure off Israel while deepening its own isolation.

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